Some verbs like わかる or ある take が instead of を to mark the "direct object" (because these verbs treat what in English is the direct object as a subject in Japanese?). For example,

サラリーマン：「課長｛かちょう｝っ、ここがわかりません！」課長：「わたしもわからん。」

Why do these verbs exist? Are there any rules to determine if a verb uses が instead of を in this way? What are some other examples of verbs like わかる or ある that use が (besides potential form verbs)?
Why can't verbs like わかる take を, or more specifically, why do verbs like わかる require having a subject to mark with が instead of having a direct object to mark with を?

2 Answers
2

Are there any rules to determine if a verb uses が instead of を in this way?

Yes there are such rules.

One of the biggest separations is whether the verb is transitive (他動詞) or intransitive (自動詞). Using を to mark the object of an action is a major characteristic of transitive verbs. わかる and ある are both intransitive, so that gives you a strong hint that を is not the right choice.

Beyond that, you can categorize verbs based on how they use が to mark various pieces of complementary information (see link at end of post.) For example, verbs of existence, verbs of state, verbs of transformation...

In the most general scenario, you just have to memorize what particles are used by what verb to add some given information to it.

why do verbs like わかる require having a subject to mark with が instead of having a direct object to mark with を?

I basically answered this question in my last paragraph, but I want to note that が arguably does not mark the subject of わかる here. For example, let's revisit your example sentence:

課長っ、ここがわかりません！

In this sentence, who is the person who does not understand? It's the speaker. So the speaker is the subject (or perhaps the "topic"), not "ここ". In this case, "ここ" is the object of the verb.

Why do these verbs exist?
That is a deep, philosophical question.
My guess is that Japanese verbs are in general conceptually independent of subjects.
A verb usually indicates some kind of action and it doesn't matter who is doing the action.
You can add a subject if you want, but it is not conceptually required.
In English you always have to attach a subject, even when it is not conceptually required.

When I say: "you always have to attach a subject", I don't mean just "you", I mean "anybody".
Unfortunately in English I cannot simply say "always have to attach a subject", without a subject. I have to artificially add the subject "you", even though I am not referring just to you.

Another example: in English there is a problem about gender-neutral sentences.http://www.kentlaw.edu/academics/lrw/grinker/LwtaGender_Neutral_Language.htm
This is a problem that only exist in languages like English that require a subject, no matter what.
In Japanese the subject is simply omitted, because many times it doesn't matter who is doing the action, the action itself is the important thing.

When I say 日本語が分かる it means "to understand Japanese".
It doesn't matter who is understanding. For the verb 分かる the only thing that matters is what is being understood.
The sentence is complete, and the meaning is conceptually complete.
You can add more information if you want, but that is optional.
You can say 私は日本語が分かる to mean "I understand Japanese".
The term 私は was added to sentence and is pretty much redundant.